Neural Processes (NPs) are a popular class of approaches for meta-learning. Similar to Gaussian Processes (GPs), NPs define distributions over functions and can estimate uncertainty in their predictions. However, unlike GPs, NPs and their variants suffer from underfitting and often have intractable likelihoods, which limit their applications in sequential decision making. We propose Transformer Neural Processes (TNPs), a new member of the NP family that casts uncertainty-aware meta learning as a sequence modeling problem. We learn TNPs via an autoregressive likelihood-based objective and instantiate it with a novel transformer-based architecture that respects the inductive biases inherent to the problem structure, such as invariance to the observed data points and equivariance to the unobserved points. We further design knobs within the TNP architecture to tradeoff the increase in expressivity of the decoding distribution with extra computation. Empirically, we show that TNPs achieve state-of-the-art performance on various benchmark problems, outperforming all previous NP variants on meta regression, image completion, contextual multi-armed bandits, and Bayesian optimization.